Table of topics and assignments 

This is a partially flipped class. This means that you are required to read and take notes from the corresponding sections of the book before the date listed in the table below. I will still go over some important points in class, but lecture time is minimized, so that there is time for group-work in class. Most important: you have to constantly solve at home all of the suggested exercises from the sections we cover. For exams (midterms and final), most of the questions will be very similar (or even identical) with problems from the suggested assignment, from the worksheets or from the examples presented in class.

Day# Date Topics Covered Suggested assignment Comments
1 8/27 1.2 Intuition vs. Proof

Worksheet 8/27		 1.2# 1, 2, 4-8all, 10, 13, 15, 16, 17* Symbol * denotes more difficult, or more theoretical problems.
Exams contain mostly standard problems, but one or two
may be like the * ones.
2 8/29 1.3 Types of Proofs
Worksheet 8/29		 1.3# 1-3, 6-19, 21-24
  
3 9/03 No class. Dorian!    
4 9/05 2.2 Odd/even, decimal representation
2.3 Divisibility rules
Worksheet 9/5		 2.2# 1-16 all
2.3# 1-16 all, 18*		 Fun puzzles for your future students in pbs. 17 and 18 in 2.2!
For Pbs 15&16 in 2.3, read the UPC label example on pages 28-29 in the text. 
5 9/10 8.3 Math. Induction and Well ordering principle
Worksheet 9/10		 8.3# 2, 3, 6, 7, 8, 11, 13, 14
6 9/12 2.5 The division algorithm
2.6 The Euclidean algorithm, gcd & lcm		 2.5# 1-5all, 7
2.6# 1-9all		  
7 9/17 More on 2.6
2.4 Prime decomposition Theorem
Facts on primes
Worksheet 9/17
2.4# 1-15all		  
8 9/19 More on 2.4
I've updated the worksheet 9/17 with the additional problem I mentioned today in class.
The whole worksheet is now a homework due Tuesday, Sep. 24.
9 9/24 2.8 Base change 2.8# 1-4all, 6*, 7  
10 9/26 2.9 Modular arithmetic
Worksheet 9/24-26		 2.9# 1-18 all Exam 1 is moved to Tuesday, Oct. 8. It covers sections 1.2, 1.3, 2.2-2.6, 2.8-2.10, 8.3.
Be sure to go over the worksheets and over all suggested problems from these sections.
Possible theoretical topics for Exam 1 (one of these proofs will be an exam question): 
Theorem 2.18, Theorem 2.30 (with Corollary 2.31), Theorem 2.16 (proof uses Corollary 2.31),
Theorem 2.32 (see pb. 5 in worksheet 9/17 for an outline of the proof).
11 10/01 2.10 Linear Diophantine Equations 2.10# 4, 8, 10 textbook and
pbs 12a, 13a, 14, 15
from this handout		 The handout is from the book "Exploring the Real Numbers" by Frederick W. Stevenson.
(second page is the one I gave you earlier in class).
12 10/03 2.7 Long Division
3.2 Polynomials - Factor Theorem		 2.7# 1-6 all (do after exam 1)
3.2# 1-20all (do after exam 1)		  
13 10/08 Exam 1    
14 10/10 3.4 Fundamental Thm. of Algebra
Viete's relations		 3.4# 1-8all
  
15 10/15 More on 3.4
Worksheet 10/15		    
16 10/17 3.5 Rational Root Theorem. Applications.
Worksheet 10/17

3.6 Quadratic formula		 3.5# 1-6all


3.6# 1, 2, 5, 9-14all		 I will not spend class time on section 3.6 Quadratic formula,
as this is a topic that you should be familiar with. You should read the material from
the textbook and solve the suggested problems. Proof of the quadratic formula is
a potential exam topic.
17 10/22 The number e
Worksheet 10/22		   Both worksheets 10/17 and 10/22 are now homeworks due
Thursday 10/24.
18 10/24 A monotone and bounded sequence is convergent.
Definitions and proof.		    
19 10/29 6.16.1 Algebraic vs. Transcendental Numbers

Worksheet 10/29		 6.16 #9, 10, 11
and Pbs. 5, 6 handout
(for 6, assume n is not a perfect square)		 This handout is one section from the wonderful book Exploring the Real Numbers,
by Frederick W. Stevenson (ISBN 0-13-040261-3). In particular, I will ask you to know
Gelfond's theorem 4.4.18 and to apply it.
Worksheet 10/29 is a homework due Thursday 11/07
20 10/31 7.2 Complex Numbers
7.7 Euler's formula
Worksheet 10/31		 7.2 #1-8 all
7.7 #3, 5, 7		  
21 11/05 7.3 Operations with cx. numbers and geometry
7.4 Polar form of cx. numbers. Roots of cx. numbers		 7.3 #4-15 all
7.4 #2-14 all		  
22 11/07 7.9 Log's of cx. numbers 7.9 #1, 2, 4-9all Exam 2 is postponed (last time!) to Tuesday, Nov. 19. It covers material done between 10/03 and 11/07
(including Log's of complex numbers).
All problems in the worksheets and all suggested exercises are potential exam questions.
Theoretical topics for Exam 2 (one of these proofs will be an exam question): 
Factor Theorem (Thm. 3.1 textbook);
Fundam. Thm. of Algebra (the easy part) (Thm 3.7 - proof of (c) as in textbook):
Rational Root Thm. (Thm. 3.12 textbook);
Quadratic formula (Example 3.18 textbook);
The proof that (1+1/n)^n is a convergent sequence (part 2 of worksheet 10/22);
Derive from Euler formula other identities (see your class-notes).
23 11/12 Mostly review for Exam 2    
24 11/14 5.2 Law of Cosines
5.3 Law of Sines (extended)
5.10.1 Heron's formula		 5.2 #1-7all (do after
5.3 #1-9all
5.10 #1-5		 The material of 5.2, 5.3, 5.10 will not appear on Exam 2.

Homework due Tuesday, Nov. 26.
25 11/19 Exam 2    
26 11/21 More on the geometry of the triangle    
27 11/26 Geometry and Optimization
Worksheet 11/26		    
28 12/03 Roller-coaster modeling problem
Worksheet 12/03		    
29 12/05 Start work on your final exam.
The Diagonal Intruder attachment (for Pb. 5)		   Final Exam is on Tuesday, Dec. 10, 9:15-11:45am in the regular room.
You have to have the written solutions completed, and present one
of the problems that you draw on that day.